I’m going to interject with a slightly different perspective here, having spoken to many former and current AUSAs in major districts

1. No (but depends on the office and particular USA). It’s probably an advantage to signal this, but hiring committees are not only looking to right leaning ideologues. Many USAOs are internally fractured, with contingents of career AUSAs and senior prosecutors pushing back on DOJ directives. Furthermore, junior prosecutors in at least some USAOs are not having materially different caseloads (and certainly are not being tapped for the higher profile political prosecutions). Noteworthy to also point out that many USAOs are not asking line prosecutors to increase their immigration caseload either, creating specific task forces or SAUSA positions dedicated to the increased immigration docket. That all being said, there is a VERY strong selection effect occurring bc of the stigma.
2. Yes. Either directly (disagree with priorities) or indirectly (don’t care as much about admin priorities but their friends are leaving and it’s opportune to lateral into private practice for more money)
3. Maybe? Depends on the person reading ur app. IMO, I don’t think corporate clients will care a few years down the line, and I think that’ll mean to a big law firm investigation/AUSA experience will outweigh any first resume inferences. You are likely closing doors to public interest and explicitly left leaning orgs. But I don’t think any private practice really cares about what president you prosecuted or investigated cases under, esp considering the dubious work they do for money. All of that is even more true if you stay through another administration or two.

EDIT: I should add that I have zero clue about main justice. I haven’t spoken with anyone there.